Séminaire de géométrie - Salle de conférences du CMLS - 10h30

The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi--Yau manifold and has been extensively studied in the context of mirror symmetry. In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role. However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.

To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation. In this talk, I will explain fundamental ideas of Berkovich geometry focusing on Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results in which I have been involved.